Compress-Forward coding with BPSK modulation for the half-duplex Gaussian relay channel

Momin Uppal, Zhixin Liu, Vladimir Stanković, Zixiang Xiong

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39 Citations (Scopus)


This paper studies compress-forward (CF) coding with BPSK modulation for the half-duplex Gaussian relay channel. In CF relaying, Wyner-Ziv coding is applied at the relay to exploit the joint statistics between signals at the relay and the destination. We propose Slepian-Wolf coded nested scalar quantization (SWCNSQ) for practical Wyner-Ziv coding at the relay. We first provide the achievable rate of SWCNSQ based CF relaying as a performance benchmark, and then present a practical code design using low-density parity-check (LDPC) codes for error protection at the source, and nested scalar quantization plus irregular-repeat accumulation (IRA) codes for CF coding at the relay. The degree distributions of the LDPC and IRA codes are optimized using extrinsic information transfer charts and Gaussian approximation. Under discretized density evolution for asymptotically large block lengths, our optimized code design operates 0.11-0.21 dB away from the SWCNSQ limit for CF relaying. Simulations with LDPC/IRA codes of length 2 × 105 bits show a performance gap of 0.27-0.38 dB from the achievable rate.

Original languageEnglish
Pages (from-to)4467-4481
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number11
Publication statusPublished - 2009
Externally publishedYes


  • BPSK modulation
  • Compress-forward
  • Distributed joint source-channel coding
  • Relay channel
  • Wyner-Ziv coding

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